on 8. However, in these experiments, approximately constant boil-up rates were maintained. To be completely quantitative, the contact angle should be determined a t a specific vapor velocity. DISCUSSION
An interesting phenomenon was observed while measuring the contact angles under conditions of mass transfer for the fluids under test. For all the positive systems studied, the sessile drop remained immobile, with no indication of interfacial turbulence occurring a t any stage in the experimental procedure. However, for the negative systems, a considerable amount of agitation was evident in the droplet, which resulted at some concentrations in the production of droplets ejected from the main sessile body. This phenomenon explains why distillation efficiencies are often high for negative systems, although the contact angle would suggest a poor wetting performance and hence low transfer area. The behavior has an analogy in liquid-liquid extraction, where systems with negative interfacial tensions produce satellite droplets.
NOMENCLATURE p = density of sessile drop g = acceleration due to gravity h = equilibrium drop height y = surface tension R = contact angle
Subscripts
L = liquid V = vapor
LITERATURE CITED Padday, J.F., "New Method for Measuring the Spreading Coefficient of a Liquid on a Solid Surface," Proc. 2nd. Intern. Congr. Surf. Act., Vol. 3, p. 136, Buttenvorths, London, 1957. Ponter, A.B., Davies, G.A., Ross, T.K., Beaton, W.I., Intern. J . Heat TFQnSfeF 10, 733 (1967). Ibid.. p. 1633. Ponter, A.B., Davies, G.A., Ross, T.K., Thornley, P.G., Ibid., 10, 349 (1967). Zuiderweg, F.J.. Harmans, A,, Chem. E r g Sei. 9, 89 (1958).
ACKNOWLEDGMENT
We acknowledge the provision of facilities by T. K . Ross and a maintenance grant to one of us (A.P.B.) from the Cabot Carbon Co., Ellesmere Port.
RECEIVEDfor review July 28, 1969. Accepted November 17, 1969.
low-Temperature Volumetric Properties of Methane ALAN J. VENNIX,' THOMAS W. LELAND, JR., a n d RlKl KOBAYASHI William Marsh Rice University, Houston, Tex. 77001 Pressure and temperature measurements were performed on 16 constant-mass methane samples ranging in density from 0.04 to 0.36 gram per cc. for temperatures between 150' and 273' K. at pressures to 680 atm. Saturation temperatures, pressures, and densities were also measured. Analysis of the data in the critical region suggested critical constants of 190.77' K., 45.66 atm., and 0.1625 gram per cc. An empirical equation of state was developed for the isochoric data which reproduces the measured pressures with an average error of 0.02% and a maximum error of 0.08%. Certain qualitative features of the isochoric equation representing the volumetric behavior of methane are discussed.
THE
pressure-volume-temperature relations for methane were determined as part of a continuing program to investigate the basic properties of gases and liquids a t low temperatures. Data have been recently reviewed and reported for hydrogen and methane in the gas phase (14, 15), helium and nitrogen in the gas phase (4, 5 ) , and low-density methane (8, 9). Available data sources for the properties of pure methane are numerous, but they are in serious disagreement, especially in the temperature region below O'C. A recent compilation by Din (6) summarizes many of the discrepancies and deficiencies of the data. Three significant investigations have been carried out on methane gas in the temperature range below 0°C. The
' Present address, Shell Development Co., Houston, Tex. 238
Journal of Chemical and Engineering Data, Vol. 15, No. 2, 1970
earliest was by Kvalnes and Gaddy (12) in 1931 a t temperatures to -70°C. and pressures to 1000 atm. Measurements by Mueller et al. (14, 15) extended the data to -128.7"C. and 510 atm. Both of these investigations claimed compressibility factors accurate to 0.1%; however, in some regions disagreements between the two sets of data are as large as 2 or 3%. Hoover et al. (8, 9) measured virial coefficients and gaseous compressibility factors between 131" and 273" K. a t pressures to 40 atm. Investigations a t temperatures above 0" C. were conducted by Michels and Nederbragt ( 1 3 ) , Schamp et al. (16),and Douslin et al. ( 7 ) . The results of all these measurements above 0°C. are in close agreement. The results reported here agree with those of Douslin et al. within 0.03% at 0°C.
For liquid methane, van Itterbeek, Verbeke, and Staes (10) in 1963 published measurements on the behavior of 14 isotherms between 114" and 190°K. a t pressures to 300 atm. The present investigation was designed to rectify the disagreement in the existing data below O'C. and to provide additional data extending into the liquid region. EXPERIMENTAL Equipment. The compressibility apparatus and procedure were described in detail in previous publications (17, 19). Briefly, the method was as follows: The methane sample was charged into a 150-cc. aluminum cylinder to a pressure of 680 atm. The cylinder, with attendant valves and lines, was weighed on a Seko analytical balance having a sensitivity of 0.1 mg. and an accuracy greater than 0.5 mg. for total masses up to 2 kg. The cylinder was then attached to a constant-volume chamber contained within a temperature-controlled bath. After charging the isochoric chamber to the desired pressure, liquid nitrogen was applied to a coil of tubing attached to the charging system. This system was then reweighed to determine the amount of methane in the measurement chamber. The isochoric vessel was a stainless steel sphere having a spherical cavity of approximately 75 cc. Connections were provided to a differential pressure cell, which was also immersed in the low-temperature bath. All the methane charged to the system could be contained in the temperature-controlled environment. About 95%-of the sample was always contained in the spherical cavity, for which accurate pressure deformation calculations could be performed. The system volume consisted of the spherical vessel, lines, valves, and the lower chamber of the differential pressure cell. This volume was measured by making a series of helium Burnett expansions ( 3 ) into a reference chamber of known volume. This reference volume was maintained a t 0" C. and the expansions were performed a t various system temperatures in order to determine directly the system volume as a function of temperature. The maximum volume error was estimated to be on the order of 0.015 cc. in a total system volume of about 7 5 cc. Pressure measurements were made with a set of calibrated dead-weight gages. Errors in the measured pressure are on the order of 0.01% a t the highest pressures and increase to about 0.07% a t the pressures as low as 1 atm. Bath temperature was controlled to &0.001" C., and the system temperature was measured with a platinum resistance thermometer embedded in the wall of the sphere to an absolute accuracy believed to be within llt0.01"C. of the recorded temperature. I n converting temperatures from C. to OK., the more recent definition of the absolute temperature scale was used, 0°C. = 273.15"K. The corresponding gas constant to be used with this new definition is R = 82.059 cc. atm./ (g. mole OK.), Details concerning the experimental apparatus are given by V ennix (17). Sample Material. The methane used was obtained commercially from the Matheson Co. and had a reported minimum purity of 99.95%. Two independent mass spectrometer measurements showed the actual purity to be in excess of 99.99%. For converting between grams and moles, a molecular weight of 16.042 was used. Compressibility Measurements. The detailed procedure for obtaining the data has been reported elsewhere (17, 19). Briefly, it consists of charging methane to the system and determining the differential mass. The temperature and pressure of the sample are measured. The bath temperature is then changed and the pressure measured for the new temperature. A series of pressure-temperature determinations was made on a constant-mass sample, beginning a t an upper limit of 0'C. and continuing by lowering the
temperature until the temperature corresponding to the vapor pressure was attained. Pressure-temperature measurements were continued along the vapor pressure curve as a further check of the experimental data. Changes in the system volume were accounted for by utilizing the measured temperature-dependence of the entire system volume and the calculated pressure deformation of a spherical chamber of known dimensions. This allowed the sample density to be determined a t any point in the pressure-temperature region studied. Due to the slight changes in volume during a series of constant-mass measurements, the density of the sample also varied slightly. I n order to obtain results a t either a constant temperature or a constant density, the original data were fitted to an empirical equation of state. This equation was used to calculate pressures and temperatures corresponding to the constant-density values reported here. The constant densities reported vary by only a few tenths of 1% from the experimentally observed densities, which show a small variation due to temperatureand pressure-induced distortion of the spherical chamber. The amount of smoothing carried out by the equation of state is thus very small and may be regarded as a correction for the distortion of the system volume. The equation of state is discussed below. The calculated pressures and temperatures for each density are presented in Table I. One additional figure more than the experimental accuracy is included in the computed pressure and temperature values to maintain internal consistency. The original experimental data before smoothing are published elsewhere (17). Vapor pressure measurements and saturated liquid densities are presented in Table 11. A comprehensive error analysis was made ( 1 7 ) , based on the estimated accuracy of the measured variablesmass, volume, pressure, and temperature. From this it was concluded that the maximum probable error in the compressibility factor varied from 0.04% in the hightemperature and -pressure region to 0.08% in the lowtemperature and -pressure region. Large-scale plots of the residual quantity, (2 - 1)/ p , showed internal consistency within 0.02%. The compressibility factor is not included in the tables, as it can be calculated from the primary variables-temperature, pressure, and density. COMPARISON WITH OTHER STUDIES
A detailed comparison was made between the data obtained in this study and other values reported. The interpolated pressures at 0" C. agreed to within 0.02% with those given by Douslin et al. (7). Data reported by Mueller (14, 15) showed average pressure deviations of 0.1% a t 255" K. and 0.4% at 200" K. Corresponding deviations in the values reported by Kvalnes and Gaddy (12) varied from an average of 0.4% at 273" K. to 2.7% a t 203" K. A comparison with the liquid data of van Itterbeek et al. (10) showed differences as high as 4%. However, the liquid density data published by these authors have reportedly been remeasured, due to inconsistencies in the original data (20). The vapor pressures in Table I1 are within 150 of the values calculated from the equation presented by Armstrong, Brickwedde, and Scott (1). Saturated liquid densities are compared in Figure 1 with the values measured by Bloomer and Parent (2) and by Keyes, Taylor, and Smith (11). Measurements conducted in the critical region are depicted in Figure 2. Figure 3 gives a large-scale cross plot of interpolated pressure-temperature values a t the overall isochoric densities. The critical point is determined by the isotherm which has an inflection point with a zero first derivative. The critical density cannot be determined by this method, since the critical isotherm is extremely flat in this region. The critical point evidenced by the Journal of Chemical and Engineering Data, Vol. 15, No. 2,
1970 239
Table I. Experimental Results Adiusted
Accuracy of original experimental measurements is discussed in text. Temp., OK.
Press., Atm.
Temp.,
o = 0.041 GramiCc.
273.380 263.393 252.821 239.777 233.522 223.802 217.833 213.009 203.059 191.816 183.147 177.178 174.668 172.506
P
50.527 48.033 45.379 42.087 40.494 38.000 36.462 35.213 32.611 29.630 27.284 25.632 24.930 24.316
o =
110.595 110.579 102.704 94.1331 88.0708 88.0449 80.5939 71.5533 59.561 44.150
99.6046 94.5228 89.3321 82.5904 75.9463 70.5128 65.833 62.094 56.874 52.030 47.700 45.110 44.398
122.246 117.806 113.005 108.966 104.199 101.215
Temp.,
Press., Atm.
OK.
p
Temp., OKK.
= 0.164 Gram/Cc.
233.362 213.012 207.822 204.003 200.541 197.891 195.124 193.489 192.043 191.787 191.395 191.197 191.008 190.807
p
163.165 137.447 127.404 110.577 92.3183 77.8210 67.651 62.618 59.215 55.151 51.883 48.641 46.699
o = 0.164 GramiCc.
273.058 273.016 252.875
169.592 169.528 139.042
p =
0.179 GramiCc.
273.092 273.071 263.118 253.141 243.119 233.137 223.155 213.180 213.172 213.165 207.531 203.030 200.867 199.181 197.265 195.076 193.215 191.840
Press., Atm.
= 0.189 GramiCc.
272.698 272.695 272.694 268.298 268.298 263.443 253.272 243.363 243.360 237.012 237.011 233.379 233.378 222.603 212.003 212.002 203.400 198.147 195.806 192.465
109.482 78.7240 70.90 75 65.204 60.039 56.111 52.017 49.609 47.502 47.137 46.571 46.287 46.008 45.735
0.158 GramiCc.
273.167 255.152 248.132 236.376 223.618 213.471 206.337 202.795 200.377 197.527 195.209 192.905 191.518
o = 0.116 GramiCc.
273.171 268.299 263.044 258.633 253.433 250.180
= 0.116 GramiCc
248.429 242.691 237.314 230.025 222.897 217.105 212.133 208.191 202.719 197.702 193.292 190.718 190.020
o = 0.104 GramiCc.
272.185 272.155 262.183 251.363 243.755 243.715 234.417 223.205 208.541 190.397
Press., Atm.
OK.
187.380 187.330 169.980 152.600 135.156 117.783 100.465 83.2477 83.2205 73.5743 65.925 62.277 59.447 56.251 52.643 49.592 47.381 47.356
p
199.744 199.746 199.748 191.360 191.366 182.075 162.664 143.763 143.765 131.671 131.674 124.753 124.736 104.294 84.3351 84.3330 68.3544 58.767 54.555 48.653
= 0.206 GramiCc.
274.151 267.309 260.100 252.960 245.904 238.529 228.077 218.591 209.262 203.539 196.471 192.346 191.421 190.671
228.227 213.066 197.057 181.188 165.489 149.163 126.043 105.201 84.8889 72.5944 57.699 49.283 47.442 45.968
730
720
7'0
a
700
u,
a
0 38
690
U w
2
0 34
680
U w
a
670
0 30
..
0
6 60
0
5
0 26
650
> L
m
6401
022
189
Y z
a CRITICAL DENSITY 0 14
I30
140
150
160
I70
880
I I)
I
1
150
200
240
193
194
,'I(
Figure 2. Experimental measurements in the critical region Critical points
Figure 1 . Saturated liquid densities C-3 This work
A
152
I91
TEMPEQATJRE
T E M P E R A T U R E , 'K
++
150
Bloomer and Parent (2) Keyes et al. ( 1 I )
Journal of Chemical and Engineering Data, Vol. 15, No. 2, 1970
K.
P. P.S.I.A.
Ref,
Nominal Density
191.06
677.1
(71)
A 190.55
668.6 671.0
(21
0.1 16 g./cc. 0.158 g./cc. 0 0.164g./cc. 0.179 g./cc. A 0.206 g./cc.
r,
0
190.77
(This work)
0 0
t o Constant Density for Methane
This number of significant figures is retained for consistency. Temp.,
Press., Atm.
OK.
Temp.,
= 0.221 Gram/&.
p
Press., Atm.
OK.
p
= 0.240
GramiCc.
Temp., OK.
p
Press., Atm.
Temp., OK.
= 0.282 GramiCc.
D
Press., Atm.
= 0.321 GramiCc.
~~
273.153 267.883 267.816 262.926 258.305 253.099 248.751 242.967 238.487 233.248 227.820 222.763 213.291 207.164 203.288 199.975 197.065 195.031 195.014 192.859 191.043 190.706 190.415 190.140 189.735 189.226 188.937 p
252.590 239.261 239.090 226.733 215.029 201.858 190.863 176.257 164.940 151.730 138.049 125.347 101.724 86.5472 77.0752 69.0424 62.074 57.255 57.221 52.187 48.024 47.256 46.600 45.978 45.075 43.950 43.310
= 0.240
275.155 268.822 260.829 253.056 245.069 236.577 228.611 221.330
682
212.903 114.797 207.594 99.2556 203.020 85.9600 199.576 76.043 194.770 62.365 191.420 53.020 188.895 46.102 187.618 42.655 p = 0.265 GramiCc. 272.981 267.880 261.819 254.520 241.276 232.788 222.864 213.636 207.737 201.010 198.385 194.385 189.227 185.237 183.322
= 0.282 GramiCc.
p
Gram/Cc.
363.591 345.060 322.956 296.286 247.754 216.544 180.109 146.323 124.749 100.400 90.8090 76.4900 58.148 44.228 37.679
274.304 266.747 258.637 250.722 240.977 233.055 224.994 217.013 208.789 200.503
299.467 280.664 256.956 233.896 210.114 184.864 161.199 139.638
431.613 400.210 366.383 333.435 292.481 259.076 224.997 191.271 156.453 121.369
1
' I
k/
6 6 0 '
012
' 013
I
014
015
'
1
016
DENSITY
017
'
018
'
019
020
GM/CC
Figure 3. interpolated isotherms in the vicinity of the critical
196.350 184.411 180.980 179.803 179.113 p
= 0.297 Gram/&
272.927 263.277 253.114 248.024 243.037 237.586 233.371 229.109 223.713 218.727 212.392 208.181 203.122 198.632 193.597 188.261 182.805 182.805 178.055 175.605 p
103.800 54.274 40.264 35.504 32.723
= 0.321
274.490 267.730 259.335 253.816 244.157 235.277 227.078 219.032
493.559 448.609 400.865 376.860 353.310 327.446 307.399 287.081 261.340 237.436 207.013 186.807 162.477 140.877 116.677 91.1138 65.081 65.107 42.664 31.186
GramiCc. 64 1.967 604.184 557.760 526.693 47 1.969 421.492 374.385 327.945
211.493 204.147 196.055 186.819 178.454 172.545 170.158 168.227 p
= 0.341 GramiCc.
252.980 247.365 235.756 228.404 212.612 204.135 197.280 189.751 181.641 176.864 172.744 159.295 p
284.074 241.068 193.510 138.986 89.4515 54.549 40.547 29.177
659.443 6F2.874 546.410 497.497 391.107 333.169 285.866 233.635 177.166 143.532 114.502 19.333
= 0.360 Gram/&
234.397 226.258 218.262 211.223 204.332 196.765 188.496 180.089 168.735 155.457 153.619 151.807 150.300
690.929 628.726 567.062 512.082 457.850 397.610 331.035 262.789 169.142 57.547 42.675 27.336 14.564
data of this work corresponds to a temperature of 190.77"K. and 45.66 atm. Estimates of the critical point made by Keyes et al. (11) and by Bloomer and Parent (2) are also shown in Figures 1 and 2. The convergence of this experimental data does not agree with either of these estimations. Both the Bloomer and Parent and Keyes determinations were made by a visual estimation of the point a t which two-phase behavior was judged to disappear. From the original data and the data of Douslin (7) above O"C., an equation of state has been developed for methane wherein a single expression for pressure as a function of density and temperature applies in both the gas and liquid region (18). This equation is as follows:
Constants for this equation with units of p.s.i.a., OK., and grams per cc. are given in Table 111. The gas constant, R, for these units is 75.174 cc. p.s.i.a. per gram OK. These constants reproduce the experimental pressure with an average absolute error of 0.04% and a root mean square error of 0.07%. The distribution of error for the 598 data points is given in Table IV. A total of only 10 points had errors in excess of 0.20%. Ninety-five per cent of the Journal of Chemical and Engineering Data, Vol. 15, No. 2, 1970
241
Table 11. Vapor Pressures and Experimental Saturated l i q u i d Densities
Table IV. Distribution of Per Cent Error in Calculated Pressure for 598 Points Number of Points
Vapor Pressures Exptl. Temp., K. press., atm. 4.4931 5.2178 5.9037 7.8865 9.7143 12.3946 14.6007 16.9027 19.7279 19.7640 23.2208 26.7224 28.7754 30.2785 33.0616 34.7192 37.7126 39.9499 42.0158 42.6514 42.9882 43.0630 43.2985 43.7285 43.7339 44.0388 44.1252 44.5913 44.8281 45.2180 45.4964 45.5038
133.730 136.409 138.726 144.417 148.821 154.309 158.213 161.861 165.876 166.017 170.407 174.332 176.443 177.953 180.688 182.179 184.703 186.524 188.113 188.593 188.801 188.919 189.063 189.413 189.383 189.612 189.674 190.011 190.177 190.455 190.653 190.658
Saturated Liquid Densities Density, Temp., K. gramicc. 0.04107 0.11607 0.15787 0.16389 0.17900 0.20644 0.22067 0.24025 0.26515 0.28186 0.29681 0.32098 0.34067 0.36001 0.37901
171.35 189.43 190.7 190.7 190.63 189.85 188.82 186.74 182.58 178.70 174.75 166.75 158.82 149.77 138.96
Table Ill. Coefficient Values for the Methane Equation of State
Coefficient A1 A? A3 A, As B1
B2 B3 B, Bs DI 0 2
D3 D4 D5 E1
E?
K F2 G TO k a
P PO
R
242
Pressure Equation -168379.37 100983.52 2074154.8 -12444994. 17600314. 369.46526 554.53908 -8614.1411 44316.430 -43179.188 -741.18776 -2806.7029 80674.262 -345392.00 382530.92 0.046002000 0.21177000 1378.7933 -1344.1846 34.348141 -147.71055 6.00000 0.141199 0.361788 0.113318 75.174
Journal of Chemical and Engineering Data, Vol. 15, No. 2, 1970
Error Range, %
in Error Range
0.00-0.05 0.05-0.10 0.10-0.15 0.15-0.20 0.20-0.30 0.30-0.40 0.40-0.50 0.50-0.60
487 79 15 7 2 3 1
4
errors were less than O . l % , the estimated accuracy of the data, indicating that the equation was reproducing the data within the limits of error of the measurements. The accuracy of the equation of state and regions of its applicability are described elsewhere (18). Except for a region near the critical point where the isotherms become flat, densities can also be predicted within 0.1%. This involves substituting a pressure and temperature into Equation l and iterating for the corresponding density. At points removed from the critical, the iteration converges rapidly to a value within 0.15 of the measured value. The equation of state has been utilized in the present paper to obtain data adjusted slightly to obtain constant values of density. For the experimental results from each charge to the cell, an average density was selected. For each experimentally measured temperature, a small pressure adjustment was then made t o give results a t this constantdensity value. The adjustment was made using the following relationship:
where Ap was the required density change and the partial derivative was evaluated from the over-all equation of state. Because the equation of state fits all of the experimental data with a precision of better than 0.1%, it is probable that these small pressure adjustments do not introduce errors larger than this value. The adjusted pressures are presented in Table I , which shows the results a t constant density. DEVIATIONS FROM ISOCHORIC LINEARITY
The precision of the data is such that it is possible to calculate the degree to which the isochoric behavior deviates from a linear or van der Waals behavior. Equation 1 was differentiated t o find dP
(7 p ) and
(E) aT2
a t each of the constant-density values nearest to an experimental measurement. The region of greatest linearity in each isochore was determined by finding the temperature, T o , and pressure, Po, a t which the second derivative is zero. No zero value of the second derivative could be determined for the p = 0.116 gram per cc. isochore or for any smaller density. The inflection point or extremum conditions for p = 0.158 gram per cc. and for all higher densities are presented in Table V. A value of zero for the second derivative indicates conditions a t which the
Temperature, Pressure, and Slope When
$
~
m (5)” =O a 2g z. (dPidT) J
Temperature, OK.
Pressure, atm.
0.341 0.321 0.297
161.23 183.00 200.60
33.033 116.341 150.380
7.085 5.923 4.814
0.158
234.61
108.053
1.431
L,
atm./”K.
(G) 3(h3 p
=-
ac
6
-
4
-
1 -
z-
3 i 2 au
2 ’ :2
O , :
Figure 4. Deviations f r o m linearity for selected methane isochores
constant-volume heat capacity is independent of isothermal density variations, because 1
-
8
a2P
Density , GramiCc.
,
IO
w
Table V. Calculated Linear lsochoric Conditions for Methane
(3)
T
A t temperatures below TOthe second derivative is positive, indicating that cu decreases with an isothermal density increase, and at temperatures above TOthe second derivative is negative, indicating that c, increases with a n isothermal density increase. Using the slope
at the point where
a linear relation, as would be predicted by the van der Waals equation of state, was calculated to give
T h e calculated value of PvdW is the result which would be predicted by van der Waals behavior at any temperature T along the isochore. The differences between the linear PvdW values and the actual experimental values are shown in Figure 4 for a few densities. A t densities where an inflection occurs, the deviation from linearity is s-shaped, with experimental pressures greater than the van der Waals pressure a t low temperatures near the saturation curve and less than the van der Waals values at high temperatures. Near the saturation curve, the magnitude of the excess of the experimental values over the van der Waals increases with increasing density u p to p = 0.221 gram per cc. At higher densities, this excess begins t o decrease, until at p = 0.341 gram per cc. the experimental value has become less than the linear van der Waals value. The deviations from linearity in the critical region at p c = 0.1625 gram per cc. are small but are definitely not zero. T h e critical isochore does not extrapolate linearly into the supercritical region, as assumed in some equations of state.
ACKNOWLEDGMENT T h e authors would like to thank the National Science Foundation for financial support of these experimental investigations, the Continental Oil Co. for a fellowship for Mr. Vennix, the Phillips Petroleum Go. for bath fluids, and Shell Oil Co. for analysis of the gas. T h e authors would like to express their appreciation to William E. Waters and Patsy S. Chappelear for their assistance with the computations.
LITERATURE CITED (1) Armstrong, G.T., Brickwedde, F.G., Scott, R.B., Jr., J . Res. Natl. Bur. Std. 55, 39 (1955). (2) Bloomer, O.T., Parent, J.D., Inst. Gas Tech. Bull. KO. 17 (1952). (3) Burnett, E.S., J . Appl. Mech. 58A, 136 (1936). (4) Canfield, F.B., Ph.D. thesis, Rice University, Houston, Tex., 1962. (5) Canfield, F.B., Leland, T.W., Kobayashi, R., Aduan. Cryog. Eng.8 , 146 (1962). (6) Din, F., “Thermodynamic Functions of Gases,” Vol. 3, pp. 60-3, Buttenvorths, London, 1961.
(7) Douslin, D.R., Harrison, R.H., Moore, R.T., McCullough, J.P., J. CHEM.ENG.DATA9, 358 (1964). (8) Hoover, A.E., Ph.D. thesis, Rice University, Houston, Tex., 1965. (9) Hoover, A.E., Nagata, I., Leland, T.W., Kobayashi, R., J . Chern. Phys. 48,2633 (1968). (10) Itterbeek, A. van, Verbeke, O., Staes, K., Physica 29, 743 (1963). (11) Keyes, F.G., Taylor, R.S., Smith, L.B., J . Math. Phys. 1, 211 (1922). (12) Kvalnes, H.M., Gaddy, V.L., J . Am. Chem. SOC. 53,394 (1931). (13) Michels, A,, Nederbragt, G.W., Physica 3, 569 (1936). (14) Mueller, W.H., Ph.D. thesis, Rice University, Houston, Tex., 1959. (15) Mueller, W.H., Leland, T.W., Kobayashi, R., A.I.Ch.E. J . 7, 267 (1961). (16) Schamp, H.W., Jr., Mason, E.A., Richardson, A.C.B., Altman, A., Phys. Fluids 1, 329 (1958). (17) Vennix, A.J., Ph.D. thesis, Rice University, Houston, Tex., 1966. (18) Vennix, A.J., Kobayashi, R., A.I.Ch.E. J . 15, p. 926 (1969). (19) Vennix, A.J., Leland, T.W., Kobayashi, R., Aduan. Cryog. Eng. 12, 700 (1966). (20) Verbeke, O., Institute of Molecular Physics, University of Maryland, private communication, 1966.
RECEIVED for review August 4, 1969. Accepted November 17, 1969.
Journal of Chemical and Engineering Data, Vol. 15, No. 2, 1970
243
